Learning from the uncertain:
semi-mechanistic models
for infectious disease dynamics


Sebastian Funk
10 May, 2018
University of Glasgow

Summer 2014

\(y=ax+b\)

\begin{eqnarray} \dot{S}&=&-\beta \frac{S}{N}I\\ \dot{I}&=&+\beta \frac{S}{N}I - \gamma I\\ \dot{R}&=&+\gamma I \end{eqnarray}

\(y=ax+b\)

"[…], Liberia and Sierra Leone will have approximately 550,000 Ebola cases (1.4 million when corrected for underreporting)"

Meltzer, 2014

What really happened

"[…], Liberia and Sierra Leone will have approximately 550,000 Ebola cases (1.4 million when corrected for underreporting)"

Meltzer, 2014

"without additional interventions or changes in community behavior (e.g., notable reductions in unsafe burial practices), the model also estimates that Liberia and Sierra Leone will have approximately 550,000 Ebola cases (1.4 million…)"

Meltzer, 2014

courtesy of Samuel V. Scarpino @svscarpino

Metcalf & Lessler (2017)

A semi-mechanistic model for real-time forecasting

The unknown

  • Community/hospital/funeral transmission
  • Spatial dynamics
  • Changes in behaviour
  • Changes in reporting
  • Interventions
  • Seasonality
  • etc

The known

  • Average incubation period (~9 days)
  • Average infectious period (~11 days)
  • Case-fatality rate (~70%)

WHO Ebola response team (2014)

Transmission intensity as a stochastic process

\(d\log(R_0(t)) = \sigma dW_t\)

Dureau (2013)

Particle MCMC

  • Method for filtering trajectories consistent with data
  • Highly parallelisable

Andrieu (2010), Murray (2013)

Assessing forecasts

Meaningful forecasts are probabilistic.

Meaningful forecasts are probabilistic.

Evaluating probabilistic forecasts requires
multiple observations.

Calibration: Compatibility of forecasts and observations.

Calibration: Compatibility of forecasts and observations.

Calibration: Compatibility of forecasts and observations.

Learning from the uncertain

Filtered trajectories tell us something about dynamics

Example: Ebola outbreak in Lofa Country, Liberia

An attempt to tease out factors that controlled Ebola

An attempt to tease out factors that controlled Ebola

Example: age of infection in childhood infections

Outlook

Forecasts are becoming part of outbreak response

Forecasting challenges

Improve forecasts by considering
all available data streams
(individual/behavioural/spatial/genetic)?

Louis du Plessis, University of Oxford (unpublished)

New tools

New tools

Bayesian inference with state-space models in R

Acknowledgements

Anton Camacho, Adam Kucharski, John Edmunds, Rachel Lowe,
Roz Eggo (LSHTM), Louis du Plessis (Oxford),
Tilmann Gneiting (Heidelberg), James Hensman (prowler.io),
Lawrence Murray (Uppsala)

Summary

Semi-mechanistic models as a way of incorporating uncertainty about the processes driving infectious disease dynamics.

  • Predictions during outbreaks
  • Identifying changes in transmission


Assessing the performance of real-time epidemic forecasts.
S.F., A. Camacho, A. J. Kucharski, R. Lowe, R. M. Eggo, W. J. Edmunds.
bioRxiv (2018) doi:10.1101/177451

Real-time forecasting of infectious disease dynamics with a stochastic semi-mechanistic model.
S.F., A. Camacho, A. J. Kucharski, R. M. Eggo, W. J. Edmunds.
Epidemics (2018) 22:56–61.

The impact of control strategies and behavioural changes on the elimination of Ebola from Lofa County, Liberia.
S.F., I. Ciglenecki, A. Tiffany, E. Gignoux et al.
Philos T R Soc B (2017) 372:1721.